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gentela July 5, 2012 03:23

Integral representation of a generic function
 
Hey guys,

I've just started reading SPH book by Liu & Liu. In second chapter, I faced with an expression which says the integral representation of a generic function is:
f(x)=int[f(x')*DeltaDirac(x-x')*dx']
I cannot understand the concept behind this formulation. Could anyone someone please help me to get through it?
you know, this is somehow none-sense for me, when x'-->x then we are going to have something like this: {f(x)=int[f(x')*1*dx'] where x=x'} so it means that
{f(x)=int[f(x)*dx]}!!!! Please correct me if I am wrong, I do appreciate your help.

FMDenaro July 5, 2012 04:25

Quote:

Originally Posted by gentela (Post 369872)
Hey guys,

I've just started reading SPH book by Liu & Liu. In second chapter, I faced with an expression which says the integral representation of a generic function is:
f(x)=int[f(x')*DeltaDirac(x-x')*dx']
I cannot understand the concept behind this formulation. Could anyone someone please help me to get through it?
you know, this is somehow none-sense for me, when x'-->x then we are going to have something like this: {f(x)=int[f(x')*1*dx'] where x=x'} so it means that
{f(x)=int[f(x)*dx]}!!!! Please correct me if I am wrong, I do appreciate your help.


No, Dirac(0) goes to infinity, is its integral to be finished and =1. That defines the function f at a position x


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